status of neutrino masses and mixing · status of neutrino masses and mixing carlogiunti...
Post on 18-Jun-2020
3 Views
Preview:
TRANSCRIPT
Status of Neutrino Masses and Mixing
Carlo Giunti
INFN, Sezione di Torino, and
Dipartimento di Fisica Teorica, Universita di Torino
giunti@to.infn.it
Torino, 28 January 2005
Introduction to Neutrino Masses, Mixing and Oscillations
Solar νe → νµ, ντ + Atmospheric νµ → ντ =⇒ 3-ν Mixing
Absolute Scale of Neutrino Masses
Cosmological Bound on Neutrino Masses
Neutrinoless Double-β Decay ⇐⇒ Majorana Mass
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 1
Neutrino Mass
Standard Model: νL, νR =⇒ no Dirac mass term ∼ νLνR (no νR , νL)
Majorana Neutrino: ν = ν
νR = νR =⇒ Majorana mass term ∼ νLνR
Standard Model: Majorana mass term not allowed by SU(2)L × U(1)Y(no Higgs triplet)
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 2
Standard Model can be estended with νR (eL, eR ; uL, uR ; dL, dR ; . . .)
νL + νR =⇒ Dirac neutrino mass term ∼ νLνR =⇒ mD . 100GeV
surprise: also Majorana neutrino mass for νR is allowed!
Lagrangian neutrino mass term ∼(νL νL
)(
0 mD
mD mMR
)(νR
νR
)
mMR can be arbitrarily large (not protected by SM symmetries)
mMR ∼ scale of new physics beyond Standard Model =⇒ mM
R À mD
diagonalization of
(0 mD
mD mMR
)
=⇒ m1 '(mD)2
mMR
, m2 ' mMR
ν2
ν1
see-saw mechanism
natural explanation of
smallness of neutrino masses
massive neutrinos are Majorana![Minkowski, PLB 67 (1977) 42; Yanagida (1979); Gell-Mann, Ramond, Slansky (1979); Mohapatra, Senjanovic, PRL 44 (1980) 912]
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 3
Standard Model: Lepton numbers are conserved
Le Lµ Lτ
(νe , e−) +1 0 0
(νµ , µ−) 0 +1 0
(ντ , τ−) 0 0 +1
Le Lµ Lτ
(νe , e+) −1 0 0
(νµ , µ+) 0 −1 0
(ντ , τ+) 0 0 −1
L = Le + Lµ + Lτ
Dirac mass term ∼ νLνR =⇒(νeL νµL ντL
)
mee meµ meτ
mµe mµµ mµτ
mτe mτµ mττ
νeR
νµR
ντR
Le , Lµ, Lτ are not conserved, but L is conserved L(ναR) = L(νβL)=⇒|∆L| = 0
Majorana mass term ∼ νLνR =⇒(νeL νµL ντL
)
mee meµ meτ
mµe mµµ mµτ
mτe mτµ mττ
νeR
νµR
ντR
L, Le , Lµ, Lτ are not conserved L(ναR) = −L(νβL)=⇒|∆L| = 2
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 4
Neutrino Oscillations
[Pontecorvo, SPJETP 6 (1957) 429] [Pontecorvo, SPJETP 7 (1958) 172] [Gribov, Pontecorvo, PLB 28 (1969) 49]
[Eliezer,Swift, NPB 105 (1976) 45] [Fritzsch, Minkowski, PLB 62 (1976) 72] [Bilenky, Pontecorvo, SJNP 24 (1976) 316]
[Bilenky, Pontecorvo, NCimL 17 (1976) 56] [Bilenky, Pontecorvo, PRep 41 (1978) 225]
Neutrino Mixing: |να〉 =∑
k
Uαk |νk〉α = e, µ, τ
νk→mk
|νk(x , t)〉 = e−iEk t+ipkx |νk〉 =⇒ |να(x , t)〉 =∑
k
Uαk e−iEk t+ipkx |νk〉
|νk〉 =∑
β=e,µ,τ
U∗βk |νβ〉
|να(x , t)〉 =∑
β=e,µ,τ
(∑
k
Uαke−iEk t+ipkxU∗βk
)
︸ ︷︷ ︸
Aνα→νβ(x ,t)
|νβ〉
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 5
Transition Probability
Pνα→νβ (x , t) = |〈νβ |να(x , t)〉|2 =
∣∣Aνα→νβ (x , t)
∣∣2 =
∣∣∣∣∣
∑
k
Uαke−iEk t+ipkxU∗βk
∣∣∣∣∣
2
ultrarelativistic neutrinos =⇒ t ' x = L source-detector distance
Ekt − pkx ' (Ek − pk) L =E 2
k − p2kEk + pk
L =m2
k
Ek + pk
L 'm2
k
2EL
Pνα→νβ (L,E ) =
∣∣∣∣∣
∑
k
Uαk e−im2kL/2E U∗
βk
∣∣∣∣∣
2
=∑
k,j
UαkU∗βkU∗
αjUβj exp
(
−i∆m2
kjL
2E
)
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 6
Two-Neutrino Mixing
|να〉 =2∑
k=1
Uαk |νk〉 (α = e, µ)
U =
(cosϑ sinϑ
− sinϑ cosϑ
)|νe〉 = cosϑ |ν1〉+ sinϑ |ν2〉
|νµ〉 = − sinϑ |ν1〉+ cosϑ |ν2〉
∆m2 ≡ ∆m221 ≡ m2
2 −m21
Transition Probability: Pνe→νµ = Pνµ→νe = sin2 2ϑ sin2(∆m2L
4E
)
Survival Probabilities: Pνe→νe = Pνµ→νµ = 1− Pνe→νµ
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 7
Solar Neutrinos
[J.N. Bahcall, http://www.sns.ias.edu/~jnb]
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 8
SNO
ΦSNOνe
= 1.76± 0.11× 106 cm−2 s−1
ΦSNOνµ,ντ = 5.41± 0.66× 106 cm−2 s−1
SNO solved
solar neutrino problem
⇓
Neutrino Physics
(April 2002)
[SNO, PRL 89 (2002) 011301, nucl-ex/0204008]
νe → νµ, ντ oscillations
⇓
Large Mixing Angle solution
∆m2 ' 5× 10−5 eV2
tan2 ϑ ' 0.4
θ2tan)2
(eV
2 m∆
10-5
10-4
10-1
1
(a)
θ2tan10
-11
90% CL95% CL99% CL99.73% CL
(b)
90%, 95%, 99%, 99.73% C.L.
[SNO, PRL 92 (2004) 181301, nucl-ex/0309004]
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 9
KamLAND
confirmation of LMA (December 2002)
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
Nob
s/N
exp
101 102 103 104 105
Distance to Reactor (m)
ILL Savannah River Bugey Rovno Goesgen Krasnoyarsk Palo Verde Chooz
KamLAND
Shade: 95% C.L. LMA
Curve:
∆m2 = 5.5× 10−5 eV2
sin2 2ϑ = 0.83
θ22sin0 0.2 0.4 0.6 0.8 1
)2 (
eV2
m∆10
-6
10-5
10-4
10-3
Rate excludedRate+Shape allowedLMAPalo Verde excludedChooz excluded
95% C.L.
[KamLAND, PRL 90 (2003) 021802, hep-ex/0212021]
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 10
Combined Fit of Solar + Reactor Neutrino Data
[KamLAND, hep-ex/0406035]
)2 (
eV2
m∆
-510
-410
θ 2tan
-110 1 10
KamLAND
95% C.L.
99% C.L.
99.73% C.L.
KamLAND best fit
Solar
95% C.L.
99% C.L.
99.73% C.L.
solar best fit
θ 2tan
0.2 0.3 0.4 0.5 0.6 0.7 0.8
)2 (
eV2
m∆
KamLAND+Solar fluxes
95% C.L.
99% C.L.
99.73% C.L.
global best fit-510×4
-510×6
-510×8
-410×1
-410×1.2
Best Fit: ∆m2 = 0.82+0.6−0.5 × 10−5 eV2 tan2 ϑ = 0.40+0.09−0.07
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 11
Atmospheric Neutrinos
N(νµ + νµ)
N(νe + νe)' 2 at E . 1GeV
uncertainty on ratios: ∼ 5%
uncertainty on fluxes: ∼ 30%
ratio of ratios
R ≡[N(νµ + νµ)/N(νe + νe)]data[N(νµ + νµ)/N(νe + νe)]MC
RKsub-GeV = 0.60± 0.07± 0.05
[Kamiokande, PLB 280 (1992) 146]
RKmulti-GeV = 0.57± 0.08± 0.07
[Kamiokande, PLB 335 (1994) 237]
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 12
Super-Kamiokande Up-Down Asymmetry
Detector
Earth
Plane tangent to S
Sample νµ path
νµ entering S
νµ exiting S
S
− any path entering the sphere S later exits
− steady state ⇒ Φin(S) = Φout(S)
− Eν & 1GeV ⇒ isotropic flux of cosmic rays
− homogeneity ⇒ Φin(s) = Φout(s), ∀s ∈ S
− D ∈ S ⇒ Φup(D) = Φdown(D),
[B. Kayser, Rev. Part. Prop., PRD 66 (2002) 010001]
(December 1998)
Aup-downνµ (SK) =
(
Nupνµ − Ndown
νµ
Nupνµ + Ndown
νµ
)
= −0.296± 0.048± 0.01
[Super-Kamiokande, Phys. Rev. Lett. 81 (1998) 1562, hep-ex/9807003]
6σ MODEL INDEPENDENT EVIDENCE OF νµ DISAPPEARANCE!
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 13
νµ → ντ Fit of Super-Kamiokande Atmospheric Data
10-3
10-2
0.7 0.75 0.8 0.85 0.9 0.95 1
sin22θ
∆m2 (
eV2 )
68% C.L.90% C.L.99% C.L.
Best Fit
∆m2 = 2.1× 10−3 eV2
sin2 2θ = 1.0
1489 live-days
April 1996 − July 2001
[Super-Kamiokande, hep-ex/0501064]
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 14
Soudan-2 & MACRO
MACRO
SOUDAN 2SK
∆m2
(eV
2 )10-1
10-2
10-3
10-4
10-50 0.2 0.4 0.6 0.8 1.0
sin2 (2θ)
[Giacomelli, Giorgini, Spurio, hep-ex/0201032]
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 15
K2Kconfirmation of atmospheric allowed region (June 2002)
10-4
10-3
10-2
0 0.2 0.4 0.6 0.8 1sin22θ
∆m2 (e
V2 )
[K2K, Phys. Rev. Lett. 90 (2003) 041801]
∆m2 (e
V2 )
68%90%99%
0 10.2 0.4 0.6 0.8sin22θ
10-2
10-3
10-1
[K2K, hep-ex/0411038]
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 16
Three-Neutrino Mixing
ναL =3∑
k=1
Uαk νkL (α = e, µ, τ)
three flavor fields νe , νµ, ντ
three massive fields ν1, ν2, ν3
∆m2SUN = ∆m2
21 ' 8.2× 10−5 eV2
∆m2ATM ' |∆m2
31| ' |∆m232| ' 2.5× 10−3 eV2
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 17
Allowed Three-Neutrino Schemes
”normal”
”inverted”
absolute scale is not determined by neutrino oscillation data
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 18
Standard Parameterization of Mixing Matrix
νeL
νµL
ντL
=
Ue1 Ue2 Ue3
Uµ1 Uµ2 Uµ3
Uτ1 Uτ2 Uτ3
ν1Lν2Lν3L
U = R23 W13 R12
=
1 0 0
0 c23 s23
0 −s23 c23
ϑ23 ' ϑATM
c13 0 s13e−iδ13
0 1 0
−s13eiδ13 0 c13
ϑ13 = ϑCHOOZ
c12 s12 0
−s12 c12 0
0 0 1
ϑ12 = ϑSUN
=
c12c13 s12c13 s13e−iδ13
−s12c23 − c12s23s13eiδ13 c12c23 − s12s23s13e
iδ13 s23c13
s12s23 − c12c23s13eiδ13 −c12s23 − s12c23s13e
iδ13 c23c13
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 19
Global Fit of Oscillation Data ⇒ Bilarge Mixing
|U|bf '
0.84 0.53 0.10
0.31− 0.43 0.56− 0.63 0.71
0.32− 0.44 0.57− 0.64 0.70
|U|3σ '
0.77− 0.88 0.46− 0.61 0.00− 0.22
0.08− 0.60 0.30− 0.79 0.55− 0.85
0.10− 0.61 0.33− 0.81 0.51− 0.83
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 20
Absolute Scale of Neutrino Masses
normal scheme
! " #
m22 = m2
1 +∆m221 = m2
1 +∆m2SUN
m23 = m2
1 +∆m231 = m2
1 +∆m2ATM
inverted scheme
$%$&
$'
$' () * +
,-.
/ 0
12 3124 &124 %1 24 '124 51 2 3
124 &124 %
124 '124 5
678 9:; 9<
= 6 9 : >: ? =@
AB >C 6
< 9 D 9 7 9 : >; 9
m21 = m2
3 −∆m231 = m2
3 +∆m2ATM
m22 = m2
1 +∆m221 ' m2
3 +∆m2ATM
Quasi Degenerate for m1 ' m2 ' m3 ' mν À√
∆m2ATM ' 5× 10−2 eV
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 21
Tritium β Decay
3H→ 3He + e− + νe
dΓ
dT=
(cosϑCGF)2
2π3|M|2 F (E) pE (Q − T )
√
(Q − T )2 −m2β
Q = M3H −M3He −me = 18.58 keV m2β =
∑
k
|Uek |2m2
k
Kurie plot: K(T ) =
√√√√√
dΓ/dT
(cosϑCGF)2
2π3|M|2 F (E) pE
=
[
(Q − T )√
(Q − T )2 −m2β
]1/2
mβ < 2.2 eV (95% C.L.)
Mainz & Troitsk[Weinheimer, hep-ex/0210050]
future: KATRIN[hep-ex/0109033] [hep-ex/0309007]
sensitivity: mβ ' 0.2− 0.3 eV
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 22
! "
#%$ & '
( )*+
, -
./ ./ 0./1 ./ 1 ./ 1 ./ 1 2
./ ./ 0
./1 ./1
./1
3435
36
78 9: ;< : = >? @ : A :
B CDE FG
H
IJ K LMN O DP Q LRS T I
36 U%V W X
Y Z[\
] ^
_` 5_` a_`b 5_` b 4_` b 6_` b c
_` 5_` a
_`b 5_`b 4
_`b 6
Quasi Degenerate: m1 ' m2 ' m3 ' mν =⇒ m2β ' m2
ν
∑
k
|Uek |2 = m2
ν
FUTURE: IF mβ . 4× 10−2 eV =⇒ NORMAL HIERARCHY
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 23
Cosmological Bound on Neutrino Masses
neutrinos are in equilibrium in primeval plasma through weak interaction reactions
νν ¿ e+e−(−)
ν e ¿(−)
ν e(−)
ν N ¿(−)
ν N νen¿ pe− νep ¿ ne+ n¿ pe−νe
weak interactions freeze out
Γweak = Nσv ∼ G 2FT 5∼T 2/MP ∼
√
GNT 4 ∼√
GNρ ∼ H=⇒ Tdec ∼ 1MeVneutrino decoupling
Relic Neutrinos: Tν =
(4
11
) 13
Tγ ' 1.945K =⇒ k Tν ' 1.676× 10−4 eV(Tγ=2.725±0.001 K)
number density: nf =3
4
ζ(3)
π2gf T
3f =⇒ nνk ,νk
' 0.1827T 3ν ' 112 cm−3
density contribution:(
ρc = 3H2
8πGN
)Ωk =
nνk ,νkmk
ρc
'1
h2mk
94.14 eV=⇒ Ων h2 =
∑
k mk
94.14 eV[Gershtein, Zeldovich, JETP Lett. 4 (1966) 120] [Cowsik, McClelland, PRL 29 (1972) 669]
h ∼ 0.7, Ων . 1 =⇒∑
k
mk . 46 eV
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 24
Power Spectrum of Density Fluctuations
[SDSS, astro-ph/0310725]
hot dark matter
prevents early galaxy formation
small scale suppression
∆P(k)
P(k)≈ −8
Ων
Ωm
≈ −0.8
(∑
k mk
1 eV
)(0.1
Ωm h2
)
for
k & knr ≈ 0.026
√mν
1 eV
√
Ωm hMpc−1
[Hu, Eisenstein, Tegmark, PRL 80 (1998) 5255]
[Dolgov, PRep 370 (2002) 33] [Kainulainen, Olive, hep-ph/0206163] [Sarkar, hep-ph/0302175] [Hannestad, NJP 6 (2004) 108]
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 25
WMAP, AJ SS 148 (2003) 175
CMB (WMAP, CBI, ACBAR) + LSS (2dFGRS) + Lyα + HST + SN-Ia
ΛCDM
T0 = 13.7± 0.1Gyr h = 0.71+0.04−0.03
Ωtot = 1.02± 0.02 Ωbh2 = 0.0224± 0.0009 Ωmh2 = 0.135+0.008−0.009
Ωνh2 < 0.0076 (95% conf.) =⇒
∑
k
mk < 0.71 eV
Hannestad, JCAP 0305 (2003) 004∑
k mk < 1.01 eV (95% conf.) WMAP+CBI+2dFGRS+HST+SN-Ia∑
k mk < 1.20 eV (95% conf.) WMAP+CBI+2dFGRS∑
k mk < 2.12 eV (95% conf.) WMAP+2dFGRS
Elgaroy and Lahav, JCAP 04 (2003) 004∑
k mk < 1.1 eV (95% conf.) WMAP+2dFGRS+HST
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 26
SDSS, PRD 69 (2004) 103501
CMB(WMAP)+LSS(SDSS)+SN-Ia
h = 0.70+0.04−0.03 Ωm = 0.30± 0.04∑
k mk < 1.7 eV (95% conf.)
SDSS, astro-ph/0406594
CMB(WMAP)+LSS(SDSS)+bias(SDSS) Pg (k) = b2 Pm(k)
Ωm = 0.25± 0.03∑
k mk < 0.54 eV (95% conf.)
SDSS, astro-ph/0407372
CMB(WMAP)+LSS(SDSS)+bias(SDSS)+Lyα(SDSS)+SN-Ia
ΩΛ = 0.72± 0.02∑
k mk < 0.42 eV (95% conf.)
Fogli, Lisi, Marrone, Melchiorri, Palazzo, Serra, Silk, hep-ph/0408045∑
k mk < 1.4 eV (2σ) CMB+LSS+HST+SN-Ia∑
k mk < 0.47 eV (2σ) CMB+LSS+HST+SN-Ia+Lyα(SDSS)
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 27
∑
k
mk . 1 eV (∼ 2σ) CMB+LSS+HST+SN-Ia
∑
k
mk . 0.5 eV (∼ 2σ) CMB+LSS+HST+SN-Ia+Lyα
!"#
$ %
&' (& ') & ') & ') &' (
& ') & ')
& ')
*+ ,- ./ - 0 12 3 - 4 -5
6 78 9: ; < <: ;= > 6
5
6 7 8 9: ; < < 6
?@ A@AB
ACAD
AD EF G H
IJK
L M
NO PN OQ CN OQ BN OQ DNO P
N OQ CN OQ B
N OQ D
FUTURE: IF∑
k
mk . 8× 10−2 eV =⇒ NORMAL HIERARCHY
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 28
Majorana Neutrino Mass?
known natural explanations
of smallness of ν masses
See-Saw Mechanism
5-D Non-Renormaliz. Eff. Operator
both imply
Majorana ν masses ⇐⇒ |∆L| = 2 ⇐⇒ ββ0ν decay
see-saw type relation mν ∼M2
EW
Mnew high energy scaleM
Majorana neutrino masses provide the most accessible
window on New Physics Beyond the Standard Model
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 29
Two-Neutrino Double-β Decay: ∆L = 0
N (A,Z)→ N (A,Z + 2) + e− + e
− + νe + νe
(T 2ν1/2)
−1 = G2ν |M2ν |2
second order weak interaction process
in the Standard Model
Neutrinoless Double-β Decay: ∆L = 2
N (A,Z )→ N (A,Z + 2) + e− + e−
(T 0ν1/2)
−1 = G0ν |M0ν |2 |mββ|
2
effective
Majorana
mass
mββ =∑
k
U2ek mk
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 30
Indication of ββ0ν Decay
[Klapdor et al., MPLA 16 (2001) 2409; FP 32 (2002) 1181; NIMA 522 (2004) 371; PLB 586 (2004) 198]
T 0ν bf1/2 = 1.19× 1025 y T 0ν
1/2 = (0.69− 4.18)× 1025 y (3σ) 4.2σ evidence
2000 2010 2020 2030 2040 20500
1
2
3
4
5
Energy, keV
Co
un
ts/k
eV
0 500 1000 1500 2000 2500 30000
10
20
30
40
50
60
70
Energy ,keV
Cou
nts
/ keV
SSE2n2b Rosen − Primakov Approximation
Q=2039 keV
pulse-shape selected spectrum 3.8σ evidence [PLB 586 (2004) 198]
the indication must be checked by other experiments
1.35 . |M0ν | . 4.12 =⇒ 0.22 eV . |mββ| . 1.6 eV
if confirmed very exciting (Majorana ν and large mass scale)
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 31
Best limits for ββ0ν Decay
Heidelberg-Moscow 76Ge [EPJA 12 (2001) 147]
T 0ν1/2 > 1.9× 1025 y (90% C.L.) =⇒ |mββ| . 0.32− 1.0 eV
IGEX 76Ge [PRD 65 (2002) 092007]
T 0ν1/2 > 1.57× 1025 y (90% C.L.) =⇒ |mββ| . 0.35− 1.1 eV
FUTURE EXPERIMENTS
NEMO3, CUORICINO, COBRA, XMASS, CAMEO, CANDLES
|mββ| ∼ few 10−1 eV
EXO, MOON, Super-NEMO, CUORE, Majorana, GEM, GERDA
|mββ| ∼ few 10−2 eV
[Zdesenko, RMP 74 (2002) 663] [Elliott,Vogel, ARNPS 52 (2002) 115] [Elliott, Engel, JPG 30 (2004) R183]
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 32
Effective Majorana Neutrino Mass in ββ0ν Decay
mββ =∑
k
U2ek mk
complex Uek ⇒ possible cancellations
mββ = |Ue1|2 m1 + |Ue2|
2 e iα21 m2 + |Ue3|2 e iα31 m3
Im[mββ]
|Ue2|2eiα21m2
|Ue3|2eiα31m3
|Ue1|2m1
mββ
Re[mββ]
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 33
General Neutrino Oscillations Bounds for ββ0ν Decay
NORMAL SCHEME
↓ H-M & IGEX ↓
m1 [eV]
|mββ|
[eV
]
10110010−110−210−310−4
101
100
10−1
10−2
10−3
10−4
NORMAL SCHEME
↓ H-M & IGEX ↓
m1 [eV]
|mββ|
[eV
]
10110010−110−210−310−4
101
100
10−1
10−2
10−3
10−4
CP violation −→
INVERTED SCHEME
↓ H-M & IGEX ↓
m3 [eV]
|mββ|
[eV
]
10110010−110−210−310−4
101
100
10−1
10−2
10−3
10−4
INVERTED SCHEME
↓ H-M & IGEX ↓
m3 [eV]
|mββ|
[eV
]
10110010−110−210−310−4
101
100
10−1
10−2
10−3
10−4
CP violation −→
FUTURE: IF |mββ| . 10−2 eV =⇒ NORMAL HIERARCHY
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 34
Indication of ββ0ν Decay
0.22 eV . |mββ| . 1.6 eV (3σ range)
OSC.
CMB+LSS+Lyα
CMB+LSS
3σ range
mν [eV]
|mββ|
[eV
]
10110010−1
101
100
10−1
tension among oscillation data, CMB+LSS+Lyα and ββ0ν signal
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 35
Summary
νe → νµ, ντ with ∆m2SUN ' 8.3× 10−5 eV2 (solar ν, KamLAND)
νµ → ντ with ∆m2ATM ' 2.4× 10−3 eV2 (atmospheric ν, K2K)
⇓
Bilarge 3ν-Mixing with |Ue3|2 ¿ 1
β Decay, Cosmology, ββ0ν Decay =⇒ mν . 1 eV
FUTURE
Theory: Why lepton mixing 6= quark mixing?
Why only |Ue3|2 ¿ 1?
Exp.: Measure |Ue3| > 0 ⇒ CP violation
Check ββ0ν signal at Quasi Degenerate mass scale
Improve bounds from β Decay, Cosmology, ββ0ν Decay
C. Giunti − Status of Neutrino Masses and Mixing − Torino, 28 January 2005 − 36
top related